Local-moment fluctuations in the optimally doped high-$T_c$ superconductor ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{6.95}$

We present results of neutron scattering experiments on ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{6.95}$ (YBCO) $\left(T_c=93\text{K}\right)$. Our results indicate that magnetic collective modes due to correlated local moments are present both above and below $T_c$ in optimally doped YBCO. The magnon-like modes are robust and not overdamped by itinerant particle-hole excitations. We compare the experimental results to predictions of the Fermi-liquid (FL) theory in the random phase approximation.

Figure 1

(Color online) Raw data and background subtraction procedure. (a,b) Scans at 52.5 and 60 meV at 10 K, 100 K, and 340 K offset by a constant for clarity. Lines are guides to for the eye. Note that the peak in (b) at 340 K is most certainly nonmagnetic. (c) Scans at 50 meV through the antiferromagnetic wave vector divided by the Bose factor. Solid lines represent smoothed data. The feature centered at $h=0.5$ at 10 and 100 K is magnetic because it is suppressed at 330 K as the underlying correlations become weaker, leaving behind a “hump” of nuclear scattering peaked at $h=0.4$. The background levels near $h=0$ and $h=1$ do not exactly match due to small nuclear contributions whose temperature dependence does not follow the Bose factor (e.g., multiphonon or incoherent elastic nuclear scattering). Linear corrections were added to the 100 and 330 K data to match the backgrounds near $h=0$ and $h=1$ with the result shown in (d). These corrections were small in all cases (the 50 meV data are the worst case); (d) 50-meV scans after adding the linear terms to the 100 and 330 K data. We assign the intensity difference between 10 K/100 K data and 330 K curve to magnetic scattering. Error bars represent s.d.

Figure 2

(Color online) Magnetic intensity at 120 K at 55 meV extracted by the procedure described in the text and Fig. 1. The data in the vicinity of equivalent AF wave vectors $\mathbf{Q}=\left(1.5,0.5,1.7\right)$ (left panel) and $\mathbf{Q}=\left(1.5,-0.5,1.7\right)$ (right panel) are shown in arbitrary units but on the same scale. Small differences between the two curves are consistent with different resolution functions at the two wave vectors and/or statistical error. This figure demonstrates that the intensity that we assign to magnetic scattering has the correct symmetry.

Figure 3

(Color online) Comparison of magnetic scattering of the ${\text{YBCO}}_{6.1}$, ${\text{YBCO}}_{6.6}$, and ${\text{YBCO}}_{6.95}$ samples. (a) Spectra of the Cu-O buckling mode scaled by the factor equal to the ratio of the volumes of the three samples. (b) Magnetic scattering intensities plotted on the same intensity scale after normalization by the volume ratio extracted from comparison of phonon intensities in (a).

Figure 4

(Color online) Magnetic intensities at different energies. (a) Magnon peak in ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{6.1}$ at 52.5 meV after subtraction of a flat background. Solid line represents the spin-wave model in Ref. 6 convoluted with the spectrometer resolution. (b–h) Magnetic scattering in ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{6.95}$ as a function of the distance from the antiferromagnetic ordering wave vector. All spectra have been normalized to the same scale. A constant background of 530 and 630 counts was subtracted in (a) and (b), respectively, whereas the other magnetic spectra were obtained as described in the text and Fig. 1. The weak broad 100-K signal at 35 meV may be an artifact of the background subtraction procedure. Error bars represent s.d. Our estimate of systematic errors given by vertical black lines is based on the temperature variation of the background.

Figure 5

(Color online) Magnetic susceptibility of ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{6.95}$. (a/b) Experimentally measured magnetic susceptibility difference between 10 K/100 K, respectively, and 300 K in the 1 1 0 direction after removing effects of the resolution. Different ad hoc functional forms were tried until their convolution with the spectrometer resolution agreed with the data. (c) Calculations based on FL/RPA (Ref. 15) for the difference between the superconducting state (10 K) and normal state (300 K). (d) RPA result for the normal state. Here the difference between 100 and 300 K is negligibly small (in contrast with experiment), so only 100-K result is shown without taking the difference. Note the logarithmic intensity scale.